Multi-antenna techniques can significantly increase the data rates and reliability of a wireless communication system. The performance is in particular improved if both the transmitter and the receiver are equipped with multiple antennas. This results in a multiple-input, multiple-output (MIMO) communication channel and such systems and/or related techniques are commonly referred to as MIMO.
Several wireless standards support MIMO antenna deployments and MIMO related techniques. FIG. 1 shows an example of a MIMO transmission system 2. The system 2 comprises a precoder 4 and NT antennas 6, where NT is an integer greater than one.
In use, a sequence of information-carrying symbol vectors sk is input to the precoder 4 to be precoded before transmission by the antennas 6 over a resource element k. The resource element k corresponds to a single use of the MIMO channel, and may for example correspond to a time interval, a particular range of frequencies, a spreading code, or any combination of one or more of these quantities. Each of the r symbols in sk belongs to a specific layer, with r (i.e. the number of layers) being known as the transmission rank. Another commonly used term for layer is symbol stream.
The symbol vector sk is multiplied in the precoder 4 by an NT×r precoding matrix Wk, thereby generating a precoded symbol vector xk. The precoded symbol vector xk is provided to the antennas 6, where it is transmitted, with each antenna transmitting one element of the precoded symbol vector xk.
The precoded symbol vector xk can thus be written as:
                              x          k                =                              [                                                                                x                    k                                          (                      1                      )                                                                                                                                        x                    k                                          (                      2                      )                                                                                                                    ⋮                                                                                                  x                    k                                          (                                              N                        T                                            )                                                                                            ]                    =                                                    [                                                                                                    W                        k                                                  (                          11                          )                                                                                                                                    W                        k                                                  (                          12                          )                                                                                                            …                                                                                      W                        k                                                  (                                                      1                            ⁢                            r                                                    )                                                                                                                                                                        W                        k                                                  (                          21                          )                                                                                                                                    W                        k                                                  (                          22                          )                                                                                                            …                                                                                      W                        k                                                  (                                                      2                            ⁢                            r                                                    )                                                                                                                                                ⋮                                                              ⋮                                                                                                                                                                          ⋮                                                                                                                          W                        k                                                  (                                                                                    N                              T                                                        ⁢                            1                                                    )                                                                                                                                    W                        k                                                  (                                                                                    N                              T                                                        ⁢                            2                                                    )                                                                                                            …                                                                                      W                        k                                                  (                                                                                    N                              T                                                        ⁢                            r                                                    )                                                                                                                    ]                            ⁡                              [                                                                                                    s                        k                                                  (                          1                          )                                                                                                                                                                        s                        k                                                  (                          2                          )                                                                                                                                                ⋮                                                                                                                          s                        k                                                  (                          r                          )                                                                                                                    ]                                      =                                          W                k                            ⁢                              s                k                                                                        (        1        )            
The precoding matrix Wk is often chosen to match the characteristics of the NR×NT MIMO channel Hk over which the signals are transmitted (where NR is the number of receiving antennas). Thus, the precoding matrix may be chosen to focus the transmit energy into a subspace which is strong in the sense of conveying as much of the transmitted energy to the receiving device as possible. In addition, the precoding matrix Wk may be chosen to orthogonalize the channel, meaning that after proper linear equalization at the receiving device, the inter-layer interference is reduced.
Subsequent to precoding, the information-carrying precoded symbol vectors are converted to time-continuous signals and amplified to produce the signals transmitted from the antennas 6. In order to avoid distortion of the signals, the amplifiers need to be dimensioned so that they can cover the dynamic range of the signals to be amplified. Peak to average power ratio (PAPR) is a measure of the relative dynamic range of a signal and it is generally desirable to keep it small (i.e. close to one) so as to minimize the requirements of the amplifiers and thus reduce cost. PAPR is one of several possible measures of the dynamic range of signal. Hereinafter, references to reduction of the PAPR of a signal are taken to mean the reduction of the dynamic range of the signal according to any measure.
One method of selecting the precoding matrix is to use a so-called “codebook” of predefined precoding matrices from which an appropriate matrix can be selected. This simplifies the selection process greatly. For example, the current version of Release 8 of the 3GPP specifications (also known as long term evolution, or LTE) specifies the following codebook when two transmit antennas are employed:
                    W        =                              W            k                    ∈                      {                                          [                                                                            1                                                                                                  1                                                                      ]                            ,                              [                                                                            1                                                                                                                          -                        1                                                                                            ]                            ,                              [                                                                            1                                                                                                  j                                                                      ]                            ,                              [                                                                            1                                                                                                                          -                        j                                                                                            ]                            ,                              [                                                                            1                                                              1                                                                                                  1                                                                                      -                        1                                                                                            ]                            ,                              [                                                                            1                                                              1                                                                                                  j                                                                                      -                        j                                                                                            ]                                      }                                              (        2        )            
The first four matrices are for a transmission rank of one. The last two matrices are for a transmission rank of two.
However, the codebook for future releases of the 3GPP specifications is undefined.